/*************************************************************************
Copyright (c) 1992-2007 The University of Tennessee.  All rights reserved.

Contributors:
    * Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to
      pseudocode.

See subroutines comments for additional copyrights.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:

- Redistributions of source code must retain the above copyright
  notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above copyright
  notice, this list of conditions and the following disclaimer listed
  in this license in the documentation and/or other materials
  provided with the distribution.

- Neither the name of the copyright holders nor the names of its
  contributors may be used to endorse or promote products derived from
  this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*************************************************************************/

#ifndef _rcond_h
#define _rcond_h

#include "ap.h"
#include "ialglib.h"

#include "lu.h"
#include "trlinsolve.h"


/*************************************************************************
Estimate of a matrix condition number (1-norm)

The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).

Input parameters:
    A   -   matrix. Array whose indexes range within [0..N-1, 0..N-1].
    N   -   size of matrix A.

Result: 1/LowerBound(cond(A))
*************************************************************************/
double rmatrixrcond1(const ap::real_2d_array& a, int n);


/*************************************************************************
Estimate of the condition number of a matrix given by its LU decomposition (1-norm)

The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).

Input parameters:
    LUDcmp      -   LU decomposition of a matrix in compact form. Output of
                    the RMatrixLU subroutine.
    N           -   size of matrix A.

Result: 1/LowerBound(cond(A))
*************************************************************************/
double rmatrixlurcond1(const ap::real_2d_array& ludcmp, int n);


/*************************************************************************
Estimate of a matrix condition number (infinity-norm).

The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).

Input parameters:
    A   -   matrix. Array whose indexes range within [0..N-1, 0..N-1].
    N   -   size of matrix A.

Result: 1/LowerBound(cond(A))
*************************************************************************/
double rmatrixrcondinf(const ap::real_2d_array& a, int n);


/*************************************************************************
Estimate of the condition number of a matrix given by its LU decomposition
(infinity norm).

The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).

Input parameters:
    LUDcmp  -   LU decomposition of a matrix in compact form. Output of
                the RMatrixLU subroutine.
    N       -   size of matrix A.

Result: 1/LowerBound(cond(A))
*************************************************************************/
double rmatrixlurcondinf(const ap::real_2d_array& ludcmp, int n);


/*************************************************************************
Obsolete 1-based version, see RMatrixRCond1 for 0-bases replacement
*************************************************************************/
double rcond1(ap::real_2d_array a, int n);


/*************************************************************************
Obsolete 1-based subroutine, see RMatrixLURCond1 for 0-based replacement.
*************************************************************************/
double rcond1lu(const ap::real_2d_array& ludcmp, int n);


/*************************************************************************
Obsolete 1-based subroutine, see RMatrixRCondInf for 0-based replacement.
*************************************************************************/
double rcondinf(ap::real_2d_array a, int n);


/*************************************************************************
Obsolete 1-based subroutine, see RMatrixLURCondInf for 0-based replacement
*************************************************************************/
double rcondinflu(const ap::real_2d_array& ludcmp, int n);


#endif
